# Factorize the Trinomial x Square Plus px Plus q

Factorize the trinomial x square plus px plus q means x2 + px +q.

In order to factorize the expression x2 + px + q, we find two numbers a and b such that (a + b) = p and ab = q.

Then, x2 + px + q = x2 + (a + b)x + ab

= x2 + ax + bx + ab

= x(x + a) + b(x + a)

= (x + a)(x + b) which are the required factors.

Solved examples to factorize the trinomial x square plus px plus q (x^2 + px + q):

1. Resolve into factors:

(i) x2 + 3x - 28

Solution:

The given expression is x2 + 3x - 28.

Find two numbers whose sum = 3 and product = - 28.

Clearly, the numbers are 7 and -4.

Therefore, x2 + 3x - 28 = x2 + 7x - 4x - 28

= x(x + 7) - 4(x + 7).

= (x + 7)(x - 4).

(ii) x2 + 8x + 15

Solution:

The given expression is x2 + 8x + 15.

Find two numbers whose sum = 8 and product = 15.

Clearly, the numbers are 5 and 3.

Therefore, x2 + 8x + 15 = x2 + 5x + 3x + 15

= x(x + 5) + 3(x + 5).

= (x + 5)(x + 3).

2. Factorize the trinomial:

(i) x2 + 15x + 56

Solution:

The given expression is x2 + 15x + 56.

Find two numbers whose sum = 15 and product = 56.

Clearly, such numbers are 8 and 7.

Therefore, x2 + 15x + 56 = x2 + 8x + 7x + 56

= x(x + 8) + 7(x + 8)

= (x + 8)(x + 7).

(ii) x2 + x - 56

Solution:

The given expression is x2 + x - 56.

Find two numbers whose sum = 1 and product = - 56.

Clearly, such numbers are 8 and - 7.

Therefore, x2 + x - 56 = x2 + 8x - 7x - 56

= x(x + 8) - 7(x + 8)

= (x + 8)(x - 7).

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